Evaluate the following limits. sin x 2x lim x→0 sin ax lim x-0 sin bx

Q: Use a graphing utility to (a) plot the graphs of the given functions, (b) find the approximate…

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Q: Compute the discriminant D(x, y) of the function. f(x, y) = x³ + y4 - 6x - 2y² +2

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Q: 6. Determine the point of intersection between the graphs f(x)=2(3)²x-1 and g(x)=3(2)³x

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Q: In estimating involved in the approximation using the Error Bound formulas. For Trapezoidal rule,…

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Q: Find the flux of the vector field V(x, y, z) = 5xy²i + 3x²yj + z³k out of the unit sphere.

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Q: L₁ = 10logio, where L,is the magnitude of sound intensity (decibels), / is the current sound…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: Graph

Q: 1. d) e) Indicate if each statement Is True or False. Write the word True or False not T or F.…

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Q: Questions #8 to #12 pertain to the accompanying Venn diagram. 10. What is the value of n(A)? a) 12…

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Q: Solve the following equations on 0≤0≤2π. 2 cos²x+3sin x = 3 tan²x-1= sec x

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Q: (c) Hence compute x6(log x)5 dx.

A: From part a we have results

Q: Find the general solution of the differential equation r' (t) = (2-7t)i + 10tj. (Use symbolic…

A: given here a differential equation and asked to find the general solution.

Q: Let r(t) = (t², 1-t, 4t). Calculate the derivative of r(t) · a(t) at t = 5 assuming that a(5) =…

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Q: For the position function s(t) = - 16t+106t, complete the following table with the appropriate…

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Q: The side of a coffee cup given by y = 2x. The base has a radius of 10cm and the top a radius of…

A: Here we have given a coffee cup with base radius of  and top radius of  and side is given by .Let,…

Q: A $4536 loan was repaid with $5978. If interest was 4.8% compounded semi-annually, for how many…

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Q: Q2 dy Find the using implicity differentiation. dx 1) a cos(xy) + e*+y

A: As per the Bartleby guidelines, answering only first question as the other questions are not the sub…

Q: 2:2 y² The point (4, k) lies on the ellipse + = 1. 32 18 Which of the following could be a value for…

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Q: 6. Evaluate limx Sin (3x) 4x

A: let

Q: 9-36 Evaluate the integral. 9. [x²³√/16 + x² dx 11. 13. X² dx dx So №o (a² + x²) ³/²³ a>0 10. 12.…

A: Given

Q: 1. Perform the indicated operation. X (1-2x)3 dx

A: We need to evaluate the following integral

Q: Find the location at t = 3 of a particle whose path satisfies = (181 +7+12+21-4) 2t r(0) = (8,7)…

A: To evaluate r(t) at t =3.

Q: Solve the initial value problem (x² - 1) y" + 4xy' + 2y = 2 롫

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Q: Consider the following. f(x) = 1 x + 7 Use the limit definition of the derivative to find the…

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Evaluate the integral. (Give your answer using component form or standard basis vectors. Express…

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Q: The slope of the line normal to the curve ex- x³ + y2 =10 at the point (0, 3) is: A. -1/6 B. 1/6 C.…

A: Equation of curve,Point

Q: Write first five terms where first term is -19 and common difference is d = -3

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Q: Evaluate the triple integral U= 2x - y 2 +2 ·√² ſ² ſ²*³² ƒ(x, y, z)dxdydz where ƒ(2, y, z) = 2 + 2 3…

A: We have to evaluate the integral.

Q: Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points…

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Q: Suppose an airplane is flying 170 mph with a heading 25° east of south (295° measured…

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Q: 1. Find the natural domain f(x) = 3 √2x+1

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Q: Simplify the trigonometric expression below by writing the simplified form in terms of sin z.…

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Q: the location at t = 3 of a particle whose path satisfies 5 dr dt - (18 18t (1 + 1)2 + 21-4) r(0) =…

A: We find the value of r(3)

Q: O O y=3x² + C y = Ce ¹/2x2 – 1 = 1/2 e*² y=C√x+3 y= +C

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Q: - Q1. Consider the function f (x) = − tan(x − π). a. Determine f '(x). b. Determine the slope of the…

A: Consider the function (a) To determine .(b) To determine the slope of the tangent to the curve  at…

Q: According to the Economist the population of Russia has been declining. The population of Russia was…

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Q: Simplify the following expressions. sin x sec x sec² x-tan²x+cot² x sin² x cos 2x-cosx sin 2x+sin x

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Q: Which of the following equations represents an ellipse with x-intercepts +2 and y-intercepts ±3? O 3…

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Q: Determine all possible values of 0, 0≤0 ≤2л, if cot 0 = -√3 cos²6 =1/12

A: We know that cos positive 1St and 4th quadrantAnd tan positive 1St and 3Rd quadrant

Q: A rate of change of H is given by d = k(5 + H). When t = 0, H = 4. When t = 3, H = 10. Solve for…

A: A rate of change of H is given by .So,        Given that t=0, H = 4 => H(0)=4and when t=3, H=10…

Q: 13. If H = {1, 2, 3, 4, 5, 7, 9, 11) and J = {1, 2, 3, 4, 6, 8, 10), then n(HUJ)= a) 4 b) 11 c) 15…

A: Note:Since you have posted multiple questions we will solve the first question for you. If you want…

Q: L₁ = 10logio where L, is the magnitude of sound intensity (decibels), and is the reference intensity…

A: The magnitude of sound intensity is given byWhere  is the reference intensity.To determine: The…

Q: 2 √√5-x² dy + xydx = 0

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Q: Find the equation of the sphere passing through P(-4, 1, 4) and Q(8, -3, 3) with its center at the…

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Q: How would I solve when it asks this? Using the same equation as previous

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Q: Find two vectors parallel to v of the given length. v=PQ with P(9,8,0) and Q(8,4,4); length = 33 The…

A: v =  with P(9, 8, 0) and Q(8, 4, 0) Also, length(L) = 33

Q: 3n (c) 201 n=1 Vn

A: To test the following series for convergence.

Q: 5. In some biological applications, population size P as a function of time t may be modeled as A 1+…

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Q: 2. Determine the absolute maximum and minimum values of f(x) on the interval -2≤x≤05. Decimals…

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Q: ( M for differentiation, which of the following c. sin (-1) u-cos^(-1) u D. -tan (-1) u+cot^(-1) u…

A: Three term given find the to reference the rule of differentiation which expression is constant.